<h2>DESCRIPTION</h2>

<em>t.select</em> performs selection of maps that are registered in 
space time datasets using temporal algebra.

<h3>PROGRAM USE</h3>
The module expects an <b>expression</b> as input parameter in the following form:
<p>
<tt>"result = expression"</tt>
<p>

The statement structure is similar to r.mapcalc, see <a href="r.mapcalc.html">r.mapcalc</a>.
Where <b>result</b> represents the name of a space time dataset 
(STDS)that will contain the result of the calculation that is given as 
<b>expression</b> on the right side of the equality sign.

These expression can be any valid or nested combination of temporal 
operations and functions that are provided by the temporal algebra.  
<br>
The temporal algebra works with space time datasets of any type 
(STRDS, STR3DS and STVDS). The algebra provides methods for map 
selection from STDS based on their temporal relations. It is also 
possible to temporally shift maps, to create temporal buffer and to 
snap time instances to create a valid temporal topology. Furthermore 
expressions can be nested and evaluated in conditional statements (if, 
else statements). Within if-statements the algebra provides temporal 
variables like start time, end time, day of year, time differences or 
number of maps per time interval to build up conditions. These 
operations can be assigned to space time datasets or to the results of 
operations between space time datasets.
<p>
The type of the input space time datasets must be defined with the input
parameter <b>type</b>. Possible options are STRDS, STVDS or STR3DS.
The default is set to space time raster datasets (STRDS).
<p>
As default, topological relationships between space time datasets will be
evaluated only temporal. Use the <b>s</b> flag to activate the
additionally spatial topology evaluation.
<p>
The expression option must be passed as <b>quoted</b>
expression, for example: <br>

<div class="code"><pre>
t.select expression="C = A : B"
</pre></div>

Where <b>C</b> is the new space time raster dataset that will contain maps
from <b>A</b> that are selected by equal temporal relationships
to the existing dataset <b>B</b> in this case.

<h2>TEMPORAL ALGEBRA</h2>

The temporal algebra provides a wide range of temporal operators and
functions that will be presented in the following section.

<h3>TEMPORAL RELATIONS</h3>

Several temporal topology relations between registered maps of space
time datasets are supported: <br>

<div class="code"><pre>
equals            A ------
                  B ------

during            A  ----
                  B ------

contains          A ------
                  B  ----

starts            A ----
                  B ------

started           A ------
                  B ----

finishs           A   ----
                  B ------

finished          A ------
                  B   ----

precedes          A ----
                  B     ----

follows           A     ----
                  B ----

overlapped        A   ------
                  B ------

overlaps          A ------
                  B   ------

over              booth overlaps and overlapped
</pre></div>

The relations must be read as: A is related to B, like - A equals B - A is
during B - A contains B <p>
Topological relations must be specified in {} parentheses. <br>

<h3>TEMPORAL OPERATORS</h3>

The temporal algebra defines temporal operators that can be combined with other 
operators to perform spatio-temporal operations. 
The temporal operators process the time instances and intervals of two temporal 
related maps and calculate the result temporal extent by five different possibilities.
<div class="code"><pre>
LEFT REFERENCE     l       Use the time stamp of the left space time dataset
INTERSECTION       i       Intersection
DISJOINT UNION     d       Disjoint union
UNION              u       Union
RIGHT REFERENCE    r       Use the time stamp of the right space time dataset
</pre></div>


<h3>TEMPORAL SELECTION</h3>

The temporal selection simply selects parts of a space time dataset without
processing raster or vector data.

The algebra provides a selection operator <b>:</b> that selects parts
of a space time dataset that are temporally equal to parts of a second one
by default. The following expression

<div class="code"><pre>
C = A : B
</pre></div>

means: Select all parts of space time dataset A that are equal to B and store
it in space time dataset C. The parts are time stamped maps. <p>
In addition the inverse selection operator <b>!:</b> is defined as the
complement of the selection operator, hence the following expression

<div class="code"><pre>
C = A !: B
</pre></div>

means: select all parts of space time time dataset A that are not equal to B
and store it in space time dataset (STDS) C. <p>
To select parts of a STDS by different topological relations to other STDS,
the temporal topology selection operator can be used. The operator consists of
the temporal selection operator, the topological relations, that must be separated 
by the logical OR operator <b>|</b> and the temporal extent operator. 
All three parts are separated by comma and surrounded by curly braces:
<div class="code"><pre>
{"temporal selection operator", "topological relations", "temporal operator"}
</pre></div>

Examples:
<div class="code"><pre>
C = A {:, equals} B
C = A {!:, equals} B
</pre></div>

We can now define arbitrary topological relations using the OR operator "|"
to connect them:

<div class="code"><pre>
C = A {:,equals|during|overlaps} B
</pre></div>

Select all parts of A that are equal to B, during B or overlaps B. <br>

In addition we can define the temporal extent of the result STDS by adding the
temporal operator.

<div class="code"><pre>
C = A {:, during,r} B
</pre></div>

Select all parts of A that are during B and use the temporal extents from B for 
C. <br>

<br>
The selection operator is implicitly contained in the temporal topology
selection operator, so that the following statements are exactly the same:

<div class="code"><pre>
C = A : B
C = A {:} B
C = A {:,equal} B
C = A {:,equal,l} B
</pre></div>

Same for the complementary selection:
<div class="code"><pre>
C = A !: B
C = A {!:} B
C = A {!:,equal} B
C = A {!:,equal,l} B
</pre></div>

<h3>CONDITIONAL STATEMENTS</h3>

Selection operations can be evaluated within conditional statements.
<br>
<div class="code"><pre>
Note A and B can either be space time datasets or expressions. The temporal 
relationship between the conditions and the conclusions can be defined at the 
beginning of the if statement. The relationship between then and else conclusion 
must be always equal.

if statement                           decision option                        temporal relations
  if(if, then, else)
  if(conditions, A)                    A if conditions are True;              temporal topological relation between if and then is equal.
  if(conditions, A, B)                 A if conditions are True, B otherwise; temporal topological relation between if, then and else is equal.
  if(topologies, conditions, A)        A if conditions are True;              temporal topological relation between if and then is explicit specified by topologies.
  if(topologies, conditions, A, B)     A if conditions are True, B otherwise; temporal topological relation between if, then and else is explicit specified by topologies.
</pre></div>
The conditions are comparison expressions that are used to evaluate
space time datasets. Specific values of temporal variables are
compared by logical operators and evaluated for each map of the STDS.<br>
<b>Important:</b> The conditions are evaluated from left to right. 

<h4>Logical operators</h4>
<div class="code"><pre>
Symbol  description

  ==    equal
  !=    not equal
  >     greater than
  >=    greater than or equal
  <     less than
  <=    less than or equal
  &&    and
  ||    or
</pre></div>

<h4>Temporal functions</h4>

The following temporal function are evaluated only for the STDS that must
be given in parenthesis.

<div class="code"><pre>
td(A)                    Returns a list of time intervals of STDS A

start_time(A)            Start time as HH::MM:SS
start_date(A)            Start date as yyyy-mm-DD
start_datetime(A)        Start datetime as yyyy-mm-DD HH:MM:SS
end_time(A)              End time as HH:MM:SS
end_date(A)              End date as yyyy-mm-DD
end_datetime(A)          End datetime as  yyyy-mm-DD HH:MM

start_doy(A)             Day of year (doy) from the start time [1 - 366]
start_dow(A)             Day of week (dow) from the start time [1 - 7], the start of the week is Monday == 1
start_year(A)            The year of the start time [0 - 9999]
start_month(A)           The month of the start time [1 - 12]
start_week(A)            Week of year of the start time [1 - 54]
start_day(A)             Day of month from the start time [1 - 31]
start_hour(A)            The hour of the start time [0 - 23]
start_minute(A)          The minute of the start time [0 - 59]
start_second(A)          The second of the start time [0 - 59]
end_doy(A)               Day of year (doy) from the end time [1 - 366]
end_dow(A)               Day of week (dow) from the end time [1 - 7], the start of the week is Monday == 1
end_year(A)              The year of the end time [0 - 9999]
end_month(A)             The month of the end time [1 - 12]
end_week(A)              Week of year of the end time [1 - 54]
end_day(A)               Day of month from the start time [1 - 31]
end_hour(A)              The hour of the end time [0 - 23]
end_minute(A)            The minute of the end time [0 - 59]
end_second(A)            The second of the end time [0 - 59]
</pre></div>

<h4>Comparison operator</h4>

The conditions are comparison expressions that are used to evaluate
space time datasets. Specific values of temporal variables are
compared by logical operators and evaluated for each map of the STDS and 
the related maps.
For complex relations the comparison operator can be used to combine conditions: 
<br>
The structure is similar to the select operator with the extension of an aggregation operator: 
{"comparison operator", "topological relations", aggregation operator, "temporal operator"}
<br>
This aggregation operator (| or &) define the behaviour if a map is related the more 
than one map, e.g for the topological relations 'contains'.
Should all (&) conditions for the related maps be true or is it sufficient to 
have any (|) condition that is true. The resulting boolean value is then compared 
to the first condition by the comparison operator (|| or &&). 
As default the aggregation operator is related to the comparison operator: <br>
Comparison operator -> aggregation operator:
<div class="code"><pre>
|| -> | and && -> & 
</pre></div>
Examples:
<div class="code"><pre>
Condition 1 {||, equal, r} Condition 2
Condition 1 {&&, equal|during, l} Condition 2
Condition 1 {&&, equal|contains, |, l} Condition 2
Condition 1 {&&, equal|during, l} Condition 2 && Condition 3
Condition 1 {&&, equal|during, l} Condition 2 {&&,contains, |, r} Condition 3
</pre></div>

<h4>Hash operator</h4>
Additionally the number of maps in intervals can be computed and used in 
conditional statements with the hash (#) operator. <br>
<div class="code"><pre>
A{#, contains}B
</pre></div>
This expression computes the number of maps from space
time dataset B which are during the time intervals of maps from
space time dataset A.<br>
A list of integers (scalars) corresponding to the maps of A
that contain maps from B will be returned. <p>
<div class="code"><pre>
C = if({equal}, A {#, contains} B > 2, A {:, contains} B)
</pre></div>
This expression selects all maps from A that temporally contains at least 2 
maps from B and stores them in space time dataset C. The leading equal statement 
in the if condition specifies the temporal relation between the if and then part 
of the if expression. This is very important, so we do not need to specify a 
global time reference (a space time dataset) for temporal processing.
<p>
Furthermore the temporal algebra allows temporal buffering, shifting
and snapping with the functions buff_t(), tshift() and tsnap()
respectively.
<div class="code"><pre>
buff_t(A, size)         Buffer STDS A with granule ("1 month" or 5)
tshift(A, size)         Shift STDS A with granule ("1 month" or 5)
tsnap(A)                Snap time instances and intervals of STDS A
</pre></div>
<br>
<h4>Single map with temporal extent</h4>
The temporal algebra can also handle single maps with time stamps in the
map function.
<div class="code"><pre>
tmap()
</pre></div>
For example:
<div class="code"><pre>
 C = A {:,during} tmap(event)
</pre></div>
This statement select all maps from space time data set A that are during
the temporal extent of single map 'event'

<br>
<h2>Examples</h2>

Select all maps from space time dataset A which have equal time stamps
with space time dataset B and C and are earlier that Jan. 1. 2005 and
store them in space time dataset D.
<div class="code"><pre>
D = if(start_date(A) < "2005-01-01", A : B : C)
</pre></div>

Select all maps from space time dataset A which contains more than three
maps of space time dataset B, else select maps from C with time
stamps that are not equal to A and store them in space time dataset D.
<div class="code"><pre>
D = if(A {#, contains} B > 3, A {:, contains} B, C)
</pre></div>

Select all maps from space time dataset B which are during the temporal
buffered space time dataset A with a map interval of three days, else
select maps from C and store them in space time dataset D.
<div class="code"><pre>
D = if(contains, td(buff_t(A, "1 days")) == 3, B, C)
</pre></div>

<h2>SEE ALSO</h2>

<em>
<a href="r.mapcalc.html">r.mapcalc</a>
</em>

<h2>REFERENCES</h2>

<a href="http://www.dabeaz.com/ply/">PLY(Python-Lex-Yacc)</a>
<p>
Gebbert, S., Leppelt, T., Pebesma, E., 2019. A topology based spatio-temporal map algebra for
big data analysis. Data 4, 86. <a href="https://doi.org/10.3390/data4020086">https://doi.org/10.3390/data4020086</a>

<h2>AUTHORS</h2>

Thomas Leppelt, S&ouml;ren Gebbert, Th&uuml;nen Institute of Climate-Smart Agriculture

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